Commercial depth sensors usually generate noisy and missing depths, especially on specular and transparent objects, which poses critical issues to downstream depth or point cloud-based tasks. To mitigate this problem, we propose a powerful RGBD fusion network, Swin-DRNet, for depth restoration. We further propose Domain Randomization-Enhanced Depth Simulation (DREDS) approach to simulate an active stereo depth system using physically based rendering and generate a large-scale synthetic dataset that contains 130K photorealistic RGB images along with their simulated depths carrying realistic sensor noises. To evaluate depth restoration methods, we also curate a real-world dataset, namely STD, that captures 30 cluttered scenes composed of 50 objects with different materials from specular, transparent, to diffuse. Experiments demonstrate that the proposed DREDS dataset bridges the sim-to-real domain gap such that, trained on DREDS, our SwinDRNet can seamlessly generalize to other real depth datasets, e.g. ClearGrasp, and outperform the competing methods on depth restoration with a real-time speed. We further show that our depth restoration effectively boosts the performance of downstream tasks, including category-level pose estimation and grasping tasks. Our data and code are available at https://github.com/PKU-EPIC/DREDS.